Probability Test

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Probability Test - 18

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Weekly Quiz Competition

Question 1
1 / -0

Poonam buys a fish from a shop for her aquarium. The shopkeeper takes out one fish at random from a tank containing $$5$$ male fish and $$8$$ female fish. What is the probability that the fish taken out is a male fish?

A
$$\displaystyle\frac{5}{13}$$

B
$$\displaystyle\frac{1}{4}$$

C
$$\displaystyle\frac{1}{5}$$

D
$$\displaystyle\frac{5}{14}$$

Solution

Favourable outcome (Getting a male fish) $$= 5$$
Total number of outcomes (Male and female fish) $$=13$$
Probability $$=\dfrac{5}{13}$$
Question 2
1 / -0

An unbiased die is thrown. The probability of getting a prime number is

A
$$ \displaystyle \frac{1}{6} $$

B
$$ \displaystyle \frac{1}{3} $$

C
$$ \displaystyle \frac{1}{2} $$

D
$$ \displaystyle \frac{2}{3} $$

Solution

Total number of outcomes = {1,2,3,4,5,6}
Favourable outcomes = {2,3,5}
Probability $$= \dfrac{3}{6} = \dfrac{1}{2}$$
Question 3
1 / -0

One card is drawn from a well-shuffled deck of $$52$$ cards. Find the probability of getting the Jack of Hearts.

A
$$\displaystyle \frac{1}{52}$$

B
$$\displaystyle \frac{1}{26}$$

C
$$\displaystyle \frac{3}{52}$$

D
None of these

Solution

Total number of outcomes $$= 52$$
Favourable outcomes (Jack of Hearts) $$= 1$$
Probability $$= \dfrac{1}{52}$$
Question 4
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There are $$30$$ tickets numbered from $$1$$ to $$30$$ in a box. A ticket is drawn at random. What is the probability that the ticket drawn bears a number which is a perfect square?

A
$$\displaystyle \frac{1}{4}$$

B
$$\displaystyle \frac{1}{3}$$

C
$$\displaystyle \frac{1}{6}$$

D
$$\displaystyle \frac{1}{8}$$

Solution

Total number of outcomes $$= 30$$
Favourable outcomes (a number which is a perfect square) $$= \{1,4,9,16,25\}$$
Probability $$=\dfrac{5}{30} = \dfrac{1}{6}$$
Question 5
1 / -0

There are $$30$$ tickets numbered from $$1$$ to $$30$$ in a box . A ticket is drawn at random. What is the probability that the ticket drawn bears an odd number?

A
$$\displaystyle \frac{1}{2}$$

B
$$\displaystyle \frac{1}{3}$$

C
$$\displaystyle \frac{2}{3}$$

D
$$\displaystyle \frac{1}{4}$$

Solution

Total number of outcomes $$= 30$$
Favourable outcomes (odd number on the ticket) $$= 15$$
Probability $$=\dfrac{15}{30} = \dfrac{1}{2}$$
Question 6
1 / -0

An unbiased die is thrown. The probability of getting a multiple of $$3$$ is

A
$$ \displaystyle \frac{1}{6} $$

B
$$ \displaystyle \frac{1}{3} $$

C
$$ \displaystyle \frac{3}{6} $$

D
$$ \displaystyle \frac{4}{6} $$

Solution

Total number of outcomes ={1,2,3,4,5,6}
Favourable outcomes ={3,6}
Probability $$=\dfrac{2}{6} = \dfrac{1}{3}$$
Question 7
1 / -0

One card is drawn from a well-shuffled deck of $$52$$ cards. Find the probability of getting a spade.

A
$$\displaystyle \frac{1}{4}$$

B
$$\displaystyle \frac{1}{3}$$

C
$$\displaystyle \frac{1}{2}$$

D
$$\displaystyle 1$$

Solution

Total number of outcomes $$= 52$$
Favourable outcomes (Spade) $$= 13$$
Probability $$= \dfrac{13}{52} = \dfrac{1}{4}$$
Question 8
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Find the probability of getting a tail when a coin is tossed once.

A
$$\displaystyle\frac{1}{6}$$

B
$$1$$

C
$$\displaystyle\frac{1}{3}$$

D
$$\displaystyle\frac{1}{2}$$

Solution

$${\textbf{Step - 1: Calculating outcomes }}$$
$$\text{Favorable outcomes i.e., getting tail = 1}$$
$${\text{Total number of outcomes [H, T] = 2}}$$
$${\textbf{Step - 2: Finding Probability }}$$
$${\textbf{The formula for probability = }}\dfrac{{{\textbf{favorable outcome}}}}{{{\textbf{total number of outcome}}}}$$
$$\text{Required probability = } \dfrac{1}{2}$$
$${\textbf{Hence , the required probability is (D) }} \mathbf{\dfrac{1}{2}}$$
Question 9
1 / -0

An unbiased die is thrown. The probability of getting a number greater than $$1$$ is

A
$$ \displaystyle \frac{1}{6} $$

B
$$ \displaystyle \frac{2}{6} $$

C
$$ \displaystyle \frac{4}{6} $$

D
$$ \displaystyle \frac{5}{6} $$

Solution

Total number of outcomes ={1,2,3,4,5,6}
Favourable outcomes ={2,3,4,5,6}
Probability $$= \dfrac{5}{6}$$
Question 10
1 / -0

The probability of getting a number greater than $$2$$ by throwing a fair dice is:

A
$$\dfrac23$$

B
$$\dfrac13$$

C
$$1$$

D
$$\dfrac35$$

Solution

S = {1, 2, 3, 4, 5, 6}
$$n(S) =6 $$
$$E = $$event of getting a number greater than $$2$$.
$$\therefore$$ E = {3, 4, 5, 6} $$\Rightarrow$$ $$n(E) = 4$$
Required prob $$= P(E) =$$ $$\displaystyle{\dfrac{n(E)}{n(S)} = \dfrac{4}{6} = \dfrac{2}{3}}$$

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Re-Attempt Weekly Quiz Competition

Probability Test - 18

Result

Probability Test - 18

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SHARING IS CARING

Question 1

$$\displaystyle\frac{5}{13}$$

$$\displaystyle\frac{1}{4}$$

$$\displaystyle\frac{1}{5}$$

$$\displaystyle\frac{5}{14}$$

Solution

Question 2

$$ \displaystyle \frac{1}{6} $$

$$ \displaystyle \frac{1}{3} $$

$$ \displaystyle \frac{1}{2} $$

$$ \displaystyle \frac{2}{3} $$

Solution

Question 3

$$\displaystyle \frac{1}{52}$$

$$\displaystyle \frac{1}{26}$$

$$\displaystyle \frac{3}{52}$$

None of these

Solution

Question 4

$$\displaystyle \frac{1}{4}$$

$$\displaystyle \frac{1}{3}$$

$$\displaystyle \frac{1}{6}$$

$$\displaystyle \frac{1}{8}$$

Solution

Question 5

$$\displaystyle \frac{1}{2}$$

$$\displaystyle \frac{1}{3}$$

$$\displaystyle \frac{2}{3}$$

$$\displaystyle \frac{1}{4}$$

Solution

Question 6

$$ \displaystyle \frac{1}{6} $$

$$ \displaystyle \frac{1}{3} $$

$$ \displaystyle \frac{3}{6} $$

$$ \displaystyle \frac{4}{6} $$

Solution

Question 7

$$\displaystyle \frac{1}{4}$$

$$\displaystyle \frac{1}{3}$$

$$\displaystyle \frac{1}{2}$$

$$\displaystyle 1$$

Solution

Question 8

$$\displaystyle\frac{1}{6}$$

$$1$$

$$\displaystyle\frac{1}{3}$$

$$\displaystyle\frac{1}{2}$$

Solution

Question 9

$$ \displaystyle \frac{1}{6} $$

$$ \displaystyle \frac{2}{6} $$

$$ \displaystyle \frac{4}{6} $$

$$ \displaystyle \frac{5}{6} $$

Solution

Question 10

$$\dfrac23$$

$$\dfrac13$$

$$1$$

$$\dfrac35$$

Solution

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